question stringlengths 72 603 | subject stringclasses 1
value | choices listlengths 4 4 | answer class label 4
classes |
|---|---|---|---|
Select the best English interpretation of the given arguments in predicate logic.
Wn ∨ Wm
(∀x)[Lx ⊃ (Dx ⊃ ~Wx)]
Ln • Dn / ~(∀x)~Wx | formal_logic | [
"Either Nancy or Marvin are at work. All lawyers are not at work if they are out to dinner. Nancy is a lawyer and out to dinner. So not everything is not at work.",
"Either Nancy or Marvin are at work. All lawyers are out to dinner if they are not at work. Nancy is a lawyer and out to dinner. So not everything is... | 0A |
Which of the following propositions is not an immediate (one-step) consequence in PL of the given premises?
I ⊃ (J ≡ K)
(J ≡ K) ⊃ (L ∨ M)
I ⊃ ~L | formal_logic | [
"~L",
"J ≡ K",
"I ⊃ (L ∨ M)",
"~L ⊃ (J ≡ K)"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
I ≡ ~J
I ∨ J / I | formal_logic | [
"Valid",
"Invalid. Counterexample when I and J are true",
"Invalid. Counterexample when I is true and J is false",
"Invalid. Counterexample when J is true and I is false"
] | 3D |
Select the best translation into predicate logic: Some folks are lucky. | formal_logic | [
"(∃x)(Fx • Lx)",
"Fl",
"Lf",
"(∀x)(Fx • Lx)"
] | 0A |
Select the best translation into predicate logic. Alexis is greeted by Ben. (a: Alexis; b: Ben; Gxy: x greets y) | formal_logic | [
"Gab",
"~Gba",
"aGb",
"Gba"
] | 3D |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
H ≡ (I · ~J)
K ≡ ~H
~(K ⊃ J) / I ≡ J | formal_logic | [
"Valid",
"Invalid. Counterexample when I, H, and K are true and J is false",
"Invalid. Counterexample when I and H are true and J and K are false",
"Invalid. Counterexample when K is true and I, H, and J are false"
] | 0A |
Construct a complete truth table for the following pairs of propositions. Then, using the truth tables, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers.
~(J ∨ K) · L and (L ⊃ J) · K | formal_logic | [
"Logically equivalent",
"Contradictory",
"Neither logically equivalent nor contradictory, but consistent",
"Inconsistent"
] | 3D |
Construct a complete truth table for the following pairs of propositions. Then, using the truth tables, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers.
(~M ⊃ ~N) ∨ (O ≡ N) and (~M · N) · [(~O ∨ ~N) · (O... | formal_logic | [
"Logically equivalent",
"Contradictory",
"Neither logically equivalent nor contradictory, but consistent",
"Inconsistent"
] | 1B |
Select the best translation into predicate logic: No senior graduates without a major. | formal_logic | [
"(∀x)(Sx ⊃ ~Gx)",
"~(∀x)(Sx ⊃ Gx)",
"(∀x)( ~Sx ⊃ ~Gx)",
"(∀x) ~(Sx ⊃ ~Gx)"
] | 0A |
Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
E ⊃ ~F
~F ⊃ G
~G | formal_logic | [
"E ⊃ F",
"F ⊃ G",
"G ⊃ E",
"~~F"
] | 3D |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(K · L) ⊃ M
N ⊃ ~M
N ∨ K / L ⊃ K | formal_logic | [
"Valid",
"Invalid. Counterexample when L, M, and N are true and K is false",
"Invalid. Counterexample when L and M are true and K and N are false",
"Invalid. Counterexample when L and N are true and K and M are false"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(G ≡ H) · ~I
~G ∨ (~H ∨ I) / G | formal_logic | [
"Valid",
"Invalid. Counterexample when H and I are true and G is false",
"Invalid. Counterexample when H is true and I and G are false",
"Invalid. Counterexample when H, I, and G are false"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~(M ≡ ~N)
M / N | formal_logic | [
"Valid",
"Invalid. Counterexample when M and N are true",
"Invalid. Counterexample when M is true and N is false",
"Invalid. Counterexample when N is true and M is false"
] | 0A |
Select the best translation into predicate logic. Some CEO is wealthier than everyone. (Cx: x is a CEO; Px: x is a person; Wxy: x is wealthier than y) | formal_logic | [
"(∃x)[Cx • (∀y)(Py • Wxy)]",
"(∃x)[Cx ⊃ (∀y)(Py ⊃ Wxy)]",
"(∃x)[Cx • (∀y)(Py ⊃ Wxy)]",
"(∀x)[Px ⊃ (∃y)(Cy ⊃ Wxy)]"
] | 2C |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
E ⊃ (F ∨ ~G)
F ⊃ (~E ∨ ~G) / ~(E ≡ F) | formal_logic | [
"Valid",
"Invalid. Counterexample when E, F, and G are true",
"Invalid. Counterexample when E and F are true and G is false",
"Invalid. Counterexample when E, F, and G are false"
] | 2C |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
H ≡ (~I ∨ J)
H ∨ ~J / ~I | formal_logic | [
"Valid",
"Invalid. Counterexample when H, I, and J are false",
"Invalid. Counterexample when H and I are true and J is false",
"Invalid. Counterexample when I is true and H and J are false"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
P ⊃ Q
Q · R / ~P · R | formal_logic | [
"Valid",
"Invalid. Counterexample when P, R, and Q are true",
"Invalid. Counterexample when P and Q are true and R is false",
"Invalid. Counterexample when R and Q are true and P is false"
] | 1B |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
J ≡ ~K
J ∨ L
~K / L | formal_logic | [
"Valid",
"Invalid. Counterexample when J and K are true and L is false",
"Invalid. Counterexample when J is true and K and L are false",
"Invalid. Counterexample when K is true and J and L are false"
] | 2C |
Which of the given formulas of PL is the best symbolization of the following sentence?
Pablo will go to the store if, and only if, his brother drives him and pays for gas. | formal_logic | [
"(P ≡ D) ≡ G",
"(D • G) ⊃ P",
"P ⊃ (D • G)",
"P ≡ (D • G)"
] | 3D |
Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
D ≡ E
F ∨ D
~E · ~F | formal_logic | [
"Inconsistent",
"Consistent. Consistent valuation when D, E, and F are true",
"Consistent. Consistent valuation when D and E are true and F is false",
"Consistent. Consistent valuation when D and F are true and E is false"
] | 0A |
Select the best translation into predicate logic: Either Taylor or Eric is a latte boy. | formal_logic | [
"Lt ∨ Le",
"Lx ∨ Ly",
"tL ∨ eL",
"Tl ⊃ El"
] | 0A |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
E ⊃ F
G ⊃ ~F / ~G ∨ ~E | formal_logic | [
"Valid",
"Invalid. Counterexample when E, F, and G are true",
"Invalid. Counterexample when E and G are true and F is false",
"Invalid. Counterexample when F and G are true and E is false"
] | 0A |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~G ⊃ H
~H / G | formal_logic | [
"Valid",
"Invalid. Counterexample when G and H are true",
"Invalid. Counterexample when G is true and H is false",
"Invalid. Counterexample when H is true and G is false"
] | 0A |
Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
A ⊃ (~B ∨ C)
C ⊃ D
A ∨ (B · ~D)
A ≡ (B ⊃ D) | formal_logic | [
"Inconsistent",
"Consistent. Consistent valuation when A and D are true and B and C are false",
"Consistent. Consistent valuation when A, B, and D are true and C is false",
"Consistent. Consistent valuation when C and D are true and A and B are false"
] | 1B |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
M ∨ N
~M · O / N | formal_logic | [
"Valid",
"Invalid. Counterexample when M and O are true and N is false",
"Invalid. Counterexample when M is true and O and N are false",
"Invalid. Counterexample when O is true and M and N are false"
] | 0A |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
P ⊃ (Q ∨ R)
(Q · S) ⊃ ~P
~(~Q ∨ R) / ~P | formal_logic | [
"Valid",
"Invalid. Counterexample when P, Q, R, and S are true",
"Invalid. Counterexample when P and Q are true and R and S are false",
"Invalid. Counterexample when P, R, and S are true and Q is false"
] | 2C |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
T ∨ U
W · T / U | formal_logic | [
"Valid",
"Invalid. Counterexample when T and W are true and U is false",
"Invalid. Counterexample when T is true and W and U are false",
"Invalid. Counterexample when W is true and T and U are false"
] | 1B |
Use the following key to translate the given formula of PL to natural, English sentences.
A: Marina reads a Percy Jackson book.
B: Izzy plays Minecraft.
C: Emily stops working.
D: Russell makes dinner.
E: Ashleigh stops by.
(~B • E) ⊃ D | formal_logic | [
"If it's not the case that both Izzy plays Minecraft and Ashleigh stops by then Russell makes dinner.",
"If it's both not the case that Izzy plays Minecraft and Ashleigh stops by then Russell makes dinner.",
"Izzy playing Minecraft and Ashleigh stopping by entails that Russell makes dinner.",
"Russell's makin... | 1B |
Construct a complete truth table for the following pairs of propositions. Then, using the truth tables, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers.
~O ⊃ P and O ∨ P | formal_logic | [
"Logically equivalent",
"Contradictory",
"Neither logically equivalent nor contradictory, but consistent",
"Inconsistent"
] | 0A |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(T · ~U) ⊃ ~W
~W ⊃ X
~Z ⊃ W
~(X · Z) / T ⊃ U | formal_logic | [
"Valid",
"Invalid. Counterexample when T, X, and Z are true and U and W are false",
"Invalid. Counterexample when T and X are true and U, W, and Z are false",
"Invalid. Counterexample when T, W, and Z are true and U and X are false"
] | 0A |
Select the best translation into predicate logic: Cecilia breaks my heart if, and only if, Maria is either a problem or a girl. | formal_logic | [
"Bc ≡ (Pm ∨ Gm)",
"Bc ≡ (Pm • Gm)",
"Bc ⊃ (Pm ∨ Gm)",
"Cb ⊃ (Pm • Gm)"
] | 0A |
Use the following key to translate the given formula of PL to natural, English sentences.
A: Marina reads a Percy Jackson book.
B: Izzy plays Minecraft.
C: Emily stops working.
D: Russell makes dinner.
E: Ashleigh stops by.
~(A ⊃ B) • (B ⊃ ~E) | formal_logic | [
"It's not the case that Marina's reading a Percy Jackson book entails that Izzy plays Minecraft, but Izzy's playing Minecraft does entail that Ashleigh doesn't stop by.",
"If Marina doesn't read a Percy Jackson book, then Izzy plays Minecraft, which entails that Ashleigh doesn't stop by.",
"Marina's reading a P... | 0A |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(A ∨ B) ⊃ C
C ⊃ ~D / D ⊃ A | formal_logic | [
"Valid",
"Invalid. Counterexample when B, C, and D are true and A is false",
"Invalid. Counterexample when B and D are true and A and C are false",
"Invalid. Counterexample when A, B, and C are false and D is true"
] | 3D |
Select the best English interpretation of the given arguments in predicate logic.
Dh ⊃ ~Pt
(∀x)Px ∨ (∀x)Mx
~Mb / ~Dh | formal_logic | [
"If my headache is dualist state, then your tickle is a physical state. Either everything is physical or everything is mental. But my broken toe is not a mental state. So my headache is not a dualist state.",
"If my headache is dualist state, then your tickle is not a physical state. Either everything is physical... | 1B |
Select the best English interpretation of the given proposition, using the following translation key: Ax: x is an apartment Hx: x is a house Lx: x is large Bxy: x is bigger than y (∃x)[Hx • (∀y)(Ay ⊃ Bxy)] | formal_logic | [
"Some houses are smaller than all apartments.",
"Every house is bigger than every apartment.",
"Some apartment is smaller than every house.",
"Some houses are bigger than every apartment."
] | 3D |
Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
A ⊃ (B • C)
~(B • C)
A ∨ (D ∨ B) | formal_logic | [
"A",
"~A",
"B",
"~B"
] | 1B |
Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
(N ⊃ ~O) ⊃ (O ∨ Q)
P ⊃ (N ⊃ ~O)
N ⊃ P | formal_logic | [
"P",
"N ⊃ ~O",
"O ∨ Q",
"~P"
] | 0A |
Select the best translation into predicate logic. Earth isn't bigger than Jupiter. (e: Earth; j: Jupiter; Bxy: x is bigger than y) | formal_logic | [
"~Bje",
"Bej",
"Bje~",
"~Bej"
] | 3D |
Identify the antecedent of the following conditional proposition: The Bees winning their first game is necessary for either the Aardvarks or the Chipmunks not winning their first game. | formal_logic | [
"The Aardvarks do not win their first game.",
"The Bees win their first game.",
"The Chipmunks do not win their first game.",
"Either the Aardvarks or the Chipmunks do not win their first game."
] | 3D |
Select the best translation into predicate logic: Some athletes don't get injured. | formal_logic | [
"~Ia",
"(∃x)(Ax • ~Ix)",
"~Ai",
"(∃x)(Ix ∨ ~Ax)"
] | 1B |
Construct a complete truth table for the following pairs of propositions. Then, using the truth tables, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers.
I ≡ ~H and ~(~I ≡ H) | formal_logic | [
"Logically equivalent",
"Contradictory",
"Neither logically equivalent nor contradictory, but consistent",
"Inconsistent"
] | 1B |
Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(T ⊃ U) ⊃ (W ⊃ U)
T ⊃ ~(U ⊃ X)
(T ⊃ ~X) ⊃ W | formal_logic | [
"Inconsistent",
"Consistent. Consistent valuation when U, W, and X are true and T is false",
"Consistent. Consistent valuation when W and X are true and T and U are false",
"Consistent. Consistent valuation when T and U are true and W and X are false"
] | 1B |
Select the best translation into predicate logic: Caroline is sweet if, and only if, Janet is engaged to Brad. | formal_logic | [
"Cs ⊃ Ej",
"Sc ≡ Ej",
"sC ≡ eJ",
"Sx ≡ Jy"
] | 1B |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either England's importing beef is a sufficient condition for France's subsidizing agriculture, or China doesn't promote human rights when and only when South Africa supplies diamonds. | formal_logic | [
"(E ⊃ F) ∨ (~C ⊃ S)",
"(F ⊃ E) ∨ (S ⊃ ~C",
"(E ⊃ F) ∨ ~(S ≡ C)",
"(E ⊃ F) ∨ (~C ≡ S)"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~K ≡ L / (K · L) ∨ (K · ~L) | formal_logic | [
"Valid",
"Invalid. Counterexample when K and L are true",
"Invalid. Counterexample when K is true and L is false",
"Invalid. Counterexample when L is true and K is false"
] | 3D |
Use the following key to translate the given formula of PL to natural, English sentences.
A: Marina reads a Percy Jackson book.
B: Izzy plays Minecraft.
C: Emily stops working.
D: Russell makes dinner.
E: Ashleigh stops by.
(~A ∨ ~B) ⊃ C | formal_logic | [
"If neither Marina reads a Percy Jackson book nor Izzy plays Minecraft, then Emily stops working.",
"If it's not the case that both Marina reads a Percy Jackson book and Izzy plays Minecraft, then Emily stops working.",
"Either Marina not reading a Percy Jackson book or Izzy not playing Minecraft entails that E... | 2C |
Identify the conclusion of the following argument. There are those who use predicate variables; the values of these variables are attributes. Predicates are wanted in all sentences regardless of whether there are attributes to refer to. The dummy predicate 'F' is wanted generally for expository purposes. If we are goi... | formal_logic | [
"There are those who use predicate variables; the values of these variables are attributes.",
"Predicates are wanted in all sentences regardless of whether there are attributes to refer to.",
"The dummy predicate 'F' is wanted generally for expository purposes.",
"If we are going to quantify over attributes a... | 3D |
Use the following key to translate the given formula of PL to natural, English sentences.
A: Marina reads a Percy Jackson book.
B: Izzy plays Minecraft.
C: Emily stops working.
D: Russell makes dinner.
E: Ashleigh stops by.
~C ∨ D | formal_logic | [
"If Emily doesn't stop working then Russell makes dinner.",
"Emily stops working unless Russell makes dinner.",
"Emily stops working unless Russell doesn't make dinner.",
"Emily doesn't stop working unless Russell makes dinner."
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~C ⊃ D
D ⊃ C / C | formal_logic | [
"Valid",
"Invalid. Counterexample when C and D are true",
"Invalid. Counterexample when C is true and D is false",
"Invalid. Counterexample when D is true and C is false"
] | 0A |
Select the best English interpretation of the given arguments in predicate logic.
(∃x)(Cx • Ox)
(∀x)[(~Cx ⊃ ~Bx) ⊃ ~Og] / ~Og | formal_logic | [
"Some cookies have oatmeal. If something's not being a cookie entails that it doesn't have chocolate chips, then this cookie doesn't have oatmeal. So this cookie doesn't have oatmeal.",
"Some cookies have oatmeal. If something is not a cookie and does not have chocolate chips, it doesn't have oatmeal. So this coo... | 0A |
Identify the conclusion of the following argument. All of psychology has gotten stuck in moral prejudices and fears. No one has come close to understanding it as the development of the will to power. However, if a person even begins to regard the effects of hatred, envy, covetousness, and the lust to rule as conditions... | formal_logic | [
"All of psychology has gotten stuck in moral prejudices and fears.",
"No one has come close to understanding it as the development of the will to power.",
"If a person even begins to regard the effects of hatred, envy, covetousness, and the lust to rule as conditions of life and furthermore, as factors essentia... | 3D |
Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
~N ≡ (O · P)
~O ⊃ Q
N · ~Q | formal_logic | [
"Inconsistent",
"Consistent. Consistent valuation when N, O, and P are true and Q is false",
"Consistent. Consistent valuation when N and O are true and P and Q are false",
"Consistent. Consistent valuation when N and P are true and O and Q are false"
] | 2C |
Which of the given formulas of PL is the best symbolization of the following sentence?
A person is considered to have lived with you for all of the present year if the person was born or died in the present year and your home was this person's home for the entire time this person was alive. | formal_logic | [
"[(B ∨ D) • H] ⊃ L",
"[L ⊃ (B ∨ D)] • H",
"L ⊃ [(B ∨ D) • H]",
"(B ∨ D • H) ⊃ L"
] | 0A |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(O ≡ P) ∨ P / P ∨ ~O | formal_logic | [
"Valid",
"Invalid. Counterexample when O and P are true",
"Invalid. Counterexample when O is true and P is false",
"Invalid. Counterexample when P is true and O is false"
] | 0A |
Which of the given formulas of PL is the best symbolization of the following sentence?
If either George enrolls or Harry enrolls, then Ira does not enroll. | formal_logic | [
"(G ⊃ H) ∨ I",
"(G ∨ H) ⊃ I",
"(G ⊃ H) ∨ ~I",
"(G ∨ H) ⊃ ~I"
] | 3D |
Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(E ⊃ F) ⊃ G
(~E ∨ F) ≡ (H ∨ I)
I ⊃ (J ⊃ ~H)
~G ⊃ ~J | formal_logic | [
"Inconsistent",
"Consistent. Consistent valuation when E is true and F, G, H, I, and J are false",
"Consistent. Consistent valuation when E and H are true and F, G, I, and J are false",
"Consistent. Consistent valuation when E and I are true and F, G, H, and J are false"
] | 1B |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~A · ~B
(A ∨ C) ∨ B / C | formal_logic | [
"Valid",
"Invalid. Counterexample when A and B are true and C is false",
"Invalid. Counterexample when A is true and B and C are false",
"Invalid. Counterexample when B is true and A and C are false"
] | 0A |
Which of the given formulas of PL is the best symbolization of the following sentence?
Brittany likes fish and lizards, but not cats. | formal_logic | [
"F • L • ~C",
"(F • L) • ~C",
"(F • L) ∨ ~C",
"C • (F • L)"
] | 1B |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~X ⊃ Y
Y ⊃ Z
~Z / ~X | formal_logic | [
"Valid",
"Invalid. Counterexample when X, Y, and Z are true",
"Invalid. Counterexample when Y and Z are true and Z is false",
"Invalid. Counterexample when X is true and Y and Z are false"
] | 3D |
S Select the best translation into predicate logic. Some kind people help some endangered species. (Ex: x is endangered; Kx: x is kind; Px: x is a person; Sx: x is a species; Hxy: x helps y) | formal_logic | [
"(∃x){(Kx • Px) • (∃y)[(Ey • Sy) • Hxy]}",
"(∃x)(∃y){[(Kx • Sx) • (Ey • Py)] • Hxy}",
"(∃x)(∃y){[(Kx • Sx) • (Ey • Py)] • Hyx}",
"(∃x)(∃y){[(Kx • Px) • (Ey • Sy)] ⊃ Hxy}"
] | 0A |
Which of the given formulas of PL is the best symbolization of the following sentence?
Everybody loves Raymond, or not. | formal_logic | [
"L",
"~L",
"L • ~L",
"L ∨ ~L"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
Q ≡ R
~(S ∨ Q) / R | formal_logic | [
"Valid",
"Invalid. Counterexample when Q and S are true and R is false",
"Invalid. Counterexample when Q is true and S and R are false",
"Invalid. Counterexample when Q, S, and R are false"
] | 3D |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
~S ∨ T
~S · U
~T ∨ U / T · U | formal_logic | [
"Valid",
"Invalid. Counterexample when S, T, and U are true",
"Invalid. Counterexample when S and U are true and T is false",
"Invalid. Counterexample when U is true and S and T are false"
] | 3D |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
L ⊃ [(M ∨ ~N) ⊃ O]
(N ⊃ O) ⊃ (~P ⊃ Q)
R ⊃ ~Q / L ⊃ (R ⊃ P) | formal_logic | [
"Valid",
"Invalid. Counterexample when L, M, O, Q, and R are true and N and P are false",
"Invalid. Counterexample when L, N, O, Q, and R are true and M and P are false",
"Invalid. Counterexample when L, N, and R are true and M, O, P, and Q are false"
] | 3D |
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